Select the statements that are true.
Given an example of a number which is divisible by:
(i) 2 but not by 4.
(ii) 3 but not by 6.
(ii) 4 but not by 8.
(iv) both 4 and 8 but not by 32.
Select the statements that are true.
Given an example of a number which is divisible by:
(i) 2 but not by 4.
(ii) 3 but not by 6.
(ii) 4 but not by 8.
(iv) both 4 and 8 but not by 32.
The correct options are
A 222 is divisible by 2.
B 50176 is divisible by 4.
C 333 is divisible by 3 but not by 6
(i) 222 is divisible by 2.
A number is divisible by 2 if its unit's digit is 0, 2, 4, 6 or 8.
The units digit of 222 is 2. Hence, 222 is divisible by 2.
(ii) Consider 50176
The number formed by the last two digits is 76, which is clearly divisible by 4.
Hence, 50176 is divisible by 4.
(ii) 333 is divisible by 3 but not by 6
A number is divisible by 3 if the sum of its digits is divisible by 3. But a number is divisible by 6 if it is divisible by both 2 and 3.
Checking divisibility by 2:
Consider the number 333
A number is divisible by 2 if its unit's digit is 0, 2, 4, 6 or 8.
The units digit of 333 is 3. Hence, 333 is not divisible by 2.
Checking divisibility by 3:
A number is divisible by 3 only when the sum of its digits is divisible by 3.
333 : 3 + 3 + 3 = 9, which is divisible by 3.
333 is not divisible by 2, but divisible by 3.
Hence, the given statement is false.
(iv) 320 is not divisible by 4
A number is divisible by 4 if the number formed by the ten's digit and unit's digit is divisible by 4.
The number formed by the last two digits is 20, which is clearly divisible by 4.
Hence, 320 is divisible by 4.
A
222 is divisible by 2.
B
50176 is divisible by 4.
C
333 is divisible by 3 but not by 6
(i) 222 is divisible by 2.
A number is divisible by 2 if its unit's digit is 0, 2, 4, 6 or 8.
The units digit of 222 is 2. Hence, 222 is divisible by 2.
(ii) Consider 50176
The number formed by the last two digits is 76, which is clearly divisible by 4.
Hence, 50176 is divisible by 4.
(ii) 333 is divisible by 3 but not by 6
A number is divisible by 3 if the sum of its digits is divisible by 3. But a number is divisible by 6 if it is divisible by both 2 and 3.
Checking divisibility by 2:
Consider the number 333
A number is divisible by 2 if its unit's digit is 0, 2, 4, 6 or 8.
The units digit of 333 is 3. Hence, 333 is not divisible by 2.
Checking divisibility by 3:
A number is divisible by 3 only when the sum of its digits is divisible by 3.
333 : 3 + 3 + 3 = 9, which is divisible by 3.
333 is not divisible by 2, but divisible by 3.
Hence, the given statement is false.
(iv) 320 is not divisible by 4
A number is divisible by 4 if the number formed by the ten's digit and unit's digit is divisible by 4.
The number formed by the last two digits is 20, which is clearly divisible by 4.
Hence, 320 is divisible by 4.
